Short answers, pulled from the story.
An ecclesiastical court, also called a court Christian or court spiritual, is a non-adversarial court conducted by church-approved officials with jurisdiction mainly in spiritual or religious matters. Historically these courts interpreted and applied canon law, with their primary legal basis in the Corpus Juris Civilis of Justinian. Their specific jurisdiction varies by denomination and era.
In the Middle Ages, ecclesiastical courts held jurisdiction over family law, dowry disputes, probate, equity, defamation, failure to observe holy days, and cases involving priests, religious communities, and public heretics. Secular courts of the same period were fragmented and decentralized, often using trial by combat or ordeal, while church courts followed more regulated inquisitorial or accusatorial procedures.
The Church of England system runs from the Archdeaconry Court at the lowest level through the bishop's court (called the Commissary Court in Canterbury and the consistory court in other dioceses), up to the Arches Court in Canterbury and the Chancery Court in York at the provincial level. In cases involving church doctrine, none of those courts has jurisdiction; those cases go to the Court of Ecclesiastical Causes Reserved. The Court of Probate Act 1857 transferred probate jurisdiction from the ecclesiastical courts to the new Court of Probate.
The Roman Rota is the tribunal of third instance in the Catholic Church's court system, hearing cases where the diocesan and metropolitan tribunals have disagreed. It consists of fifteen judges called auditors who sit in panels of three. Above the Rota stands the Apostolic Signatura, a panel of five cardinals that serves as the highest court in the Roman Catholic Church.
The Apostolic Penitentiary is a Catholic tribunal with jurisdiction only over secret matters, including what is confessed in the Sacrament of Penance. Cases are brought before it by a confessor who writes using standardized Latin pseudonyms to protect the penitent's identity. The Cardinal Major Penitentiary, acting in the Pope's name, empowers the confessor to impose a penance and lift applicable penalties.
The Judicial Council is the highest court in the United Methodist Church, composed of nine members, both laity and clergy, elected by the General Conference for eight-year terms. It interprets the Book of Discipline between General Conference sessions, rules on the constitutionality of legislation passed during those sessions, and hears appeals from clergy facing defrocking or revocation of membership. The council meets twice a year at various locations throughout the world.